DATA

We observed two-photon absorption of wavelengths as low as 6377 Å, corresponding to a two-photon transition from the ground state (5p⁶6s²) to the 48d excited state, and as high as 6689 Å, corresponding to a transition from the ground state to the 11d excited state.  Absorption lines are shown in the following graph:

The dip at the far left of the first graph is merely the signal going to zero as we calibrated the signal. Absorption lines corresponding to s state and d state transitions alternate.  The more intense lines represent transitions form the ground satae to the d states; the less intense lines represent transitions form the ground satae to the s states.  The lines on the second graph are lower and the graph's shape is distorted due to hasty data collection while the Cesium was still heating up. Nevertheless, their positions are most important.  Using the positions of these lines, we calculated the energies for various transitions and compiled them in a table of Transition Energies for Cesium.

The Transition Energy corresponds to twice the energy of each incident photon, since two photons are aborbed simutaneously. Comparing our data with some of the energy levels in Charlotte Moore's Atomic Enery Levels, we found that each of the transition energies we determined experimentally were about 3 to 5 wavenumbers above the book value.  Since this error is consistent throughout our data, this indicates the presence of a systematic error in taking data. We think this most likely occured while converting the dye laser dial reading to a wavelength in angstroms. 

Each electron can be either spin up or spin down.   Because of the spin, the electrons have spin angular momentum and a spin magnetic moment caused by the spin.  Electron spin, however, can have only two orientations with respect to the z-axis.  Because of this restriction, the spin magnetic moment can have only two orientations. 

One goal of our experiment was to calculate the quantum defect for Cesium:

We calculate this value in two ways.  First, using the value of R=1.097* 10^5 cm-1 for the Rydberg constant, we calculated the quantum defects for each level by simply using the book value of the ioniztion energy (31398).   This determines the quantum defect for each level based on the relation between that energy and the ionization energy. Theoretically, the defect should decrease for higher energy levels, yet it should not dip below zero, as it does in the second graph.  We believe the obvious fallacy in these quantum defects results from the systematic error in our data.   Because of the error, the energy levels we calculated would not converge to 31398 were we able to find their limit.

To get around this error (or at least look at it from a different perspective), we attempted to calculate the defect by looking at the differences between adjacent levels rather than the difference between one level and the ionization level (n=infinity). We fit our data to the Rydberg formula:

Energy En is energy change from two photon absorption.  The energy T is energy level limit (near  ionization energy of the atom).  For Cesium, T=31398 cm-1 (Moore).  Knowing two energies from two different states, we were able to elimate the "erroneous" T and have an equation that could be solved for the quantum defect:

Solving the equation using Mathematica, we obtained values for the quantum defect for each level.  If the data fits the Rydberg relation, a graph of En versus 1/(n-d)^2 should be linear with slope of -R and should intersect the y-axis at T=31398.  If the graph is linear, then the Rydberg relation does fit the data.  For our data, we found that the graph was indeed linear, yet the intercept did not correspond with the book value for the energy T (31398 cm-1). Also, the slope of the line came out slightly differnt from the Rydberg constant.  Resulting from the systematic error previously discussed, the graphs indicate that our energy calculations are all slightly above the true values, since the shift in the y-axis intercept is almost identical for both the d-series and the s-series.  This problem could easily result form improper calibration of the dye laser dial.

S States

D States

Calculating the quantum defect from the energy differences between adjacent levels, we should expect the values to be more constant and to not drop below zero.  This did occur:

S States

D States

The quantum defects for both series are much more constant than in the first calculation.  In the d series, they hover around 2.6 and for the s series the defects are generally near 5.12 .  The accepted values for the quantum defects for Cesium are 4.06 for the s series and 2.46 for the d serie (Hezel 329).  Thus, this method of calculation gave us a values very near the accepted values, though not without error.

DCM Dye laser output:

Table of Contents:

1. Main Menu
2. Theory: Multi-photon absorption and Raman Scattering 
3. Data
4. Energy Levels
5. Procedure and Aparatus